arXiv subjects

Farook Rahaman

Publications and source records attributed to Farook Rahaman.

At least 73 records · Page 4Linked to original sources

arXiv2020

An analytical anisotropic compact stellar model of embedding class I

A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration has unequal principal stresses i.e. fluid is locally anisotropic. A certain physically motivated geometry of metric potential has been chosen and codependency of the metric potentials outlines the formation of the model. The exterior spacetime is assumed as described by the exterior Schwarzschild solution. The smooth matching of the interior to the exterior Schwarzschild spacetime metric across the boundary and the condition that radial pressure is zero across the boundary lead us to determine the model parameters. Physical requirements and stability analysis of the model demanded for a physically realistic star are satisfied. The developed model has been investigated graphically by exploring data from some of the known compact objects. The mass-radius (M-R) relationship that shows the maximum mass admissible for observed pulsars for a given surface density has also been investigated. Moreover, the physical profile of the moment of inertia (I) thus obtained from the solutions is confirmed by the Bejger-Haensel concept.

gr-qc↗

arXiv2020

A new model for dark matter fluid sphere

We develop a new model for a spherically symmetric dark matter fluid sphere containing two regions: {\bf (i)} Isotropic inner region with constant density and {\bf (ii)} Anisotropic outer region. We solve the system of field equation by assuming a particular density profile along with a linear equation of state. The obtained solutions are well-behaved and physically acceptable which represent equilibrium and stable matter configuration by satisfying the TOV equation and causality condition, condition on adiabatic index, Harrison-Zeldovich-Novikov criterion, respectively. We consider the compact star EXO 1785-248 (Mass $M=1.3~M_{\odot}$ and radius $R = 8.8 ~km.$) to analyze our solutions by graphical demonstrations.

gr-qc↗

arXiv2020

Geodesic stability and Quasi normal modes via Lyapunov exponent for Hayward Black Hole

We derive proper-time Lyapunov exponent $(λ_{p})$ and coordinate-time Lyapunov exponent $(λ_{c})$ for a regular Hayward class of black hole. The proper-time corresponds to $τ$ and the coordinate time corresponds to $t$. Where $t$ is measured by the asymptotic observers both for for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as $\frac{λ_{p}}{λ_{c}} = \frac{(r_σ^{3} + 2 l^{2} m )}{\sqrt{(r_σ^{2} + 2 l^{2} m )^{3}- 3 m r_σ^{5}}}$ for time-like geodesics. In the limit of $l=0$ that means for Schwarzschild black hole this ratio reduces to $\frac{λ_{p}}{λ_{c}} = \sqrt{\frac{r_σ}{(r_σ-3 m)}}$. Using Lyponuov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time-scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes~(QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.

gr-qc↗

arXiv2020

Conformally symmetric traversable wormholes in $f(R,T)$ gravity

To find more deliberate $f(R, T)$ astrophysical solutions, we proceed by studying wormhole geometries under the assumption of spherical symmetry and the existence of a conformal Killing symmetry to attain the more acceptable astrophysical results. To do this, we consider a more plausible and simple model $f(R,T)=R+2χT$, where $R$ is the Ricci scalar and $T= -ρ+p_r+2p_t$ denotes the trace of the energy-momentum tensor of the matter content. We explore and analyze two cases separately. In the first part, wormhole solutions are constructed for the matter sources with isotropic pressure. However, the obtained solution does not satisfy the required wormhole conditions. In the second part, we introduce an EoS relating with pressure (radial and lateral) and density. We constrain the models with phantom energy EoS i.e. $ω= p_r/ ρ< -1$, consequently violating the null energy condition. Next, we analyze the model via $p_t= n p_r $. Several physical properties and characteristics of these solutions are investigated which are consistent with previous references about wormholes. We mainly focus on energy conditions (NEC, WEC and SEC) and consequently for supporting the respective wormhole geometries in details. In both cases it is found that the energy density is positive as seen by any static observer. To support the theoretical results, we also plotted several figures for different parameter values of the model that helps us to confirm the predictions. Finally, the volume integral quantifier, which provides useful information about the total amount of exotic matter required to maintain a traversable wormhole is discussed briefly.

gr-qc↗

arXiv2020

Tolman IV fluid sphere in bigravity

We present Tolman IV spacetime representing compact fluid sphere in bigravity. Here we have explored the effect of scale parameter $k$ in the local matter distribution of compact stars. We have model for three well-known compact stars and it shows that for lower values of $k$ leads to stiffer EoS. This claim is also supported by the graphical analysis. It can be observed that the sound speed and the adiabatic index are more for lower values of $k$. It is also seen that all the solutions of Einstein's field equations are still satisfying the field equations in the presence of a background metric $γ_{μν}$. However, the density and pressure does modified by extra term from the constant curvature background, thus affecting the EoS. One can also think that the parameter $α\equiv 1/k^2$ as coupling constant between the $g_{μν}$ and $γ_{μν}$ and consequently more the coupling stiffer is the EoS. As $k\rightarrow \infty$, the background de-Sitter spacetime reduces to Minkowski's spacetime and the coupling vanishes. The solution satisfy the causality condition, all the energy conditions and equilibrium under gravity and hydrostatic forces. The stability of the local stellar structure is enhanced by reducing the scalar curvature of the background spacetime.

gr-qc↗

arXiv2020

Compact stars with exotic matter

In this paper we employ Tolman VII solution with exotic matter that may be present in the extremely dense core of compact objects. The Tolman VII solution, an exact analytic solution to the spherically symmetric, static Einstein field equations with a perfect fluid source, has many characteristics that make it interesting for modeling high density stellar astronomical objects. For our purpose we use generalized non-linear equation of state which may incorporate exotic matter along with dust, radiation and dark energy. The equation of state (EoS) has a linear contribution comprising quark/radiation matters and a nonlinear contribution comprising dark energy/exotic matters. The amount of exotic matter contain can be modify by a parameter $n$ which can be linked to adiabatic index. As $n$ increases the exotic contribution increases which stiffens the EoS. The physical properties of the model such as pressure, density, mass function, surface redshift, gravitational redshift are examined and the stability of the stellar configuration is discussed in details. The model has promising features as it satisfies all energy conditions and is free from central singularities. The $M-R$ relation is constructed analytically and the maximum mass and its corresponding radius is determined using the exact solutions and is shown to satisfy various observational stellar compact stars.

gr-qc↗

arXiv2020

Singularity-free nonexotic compact star in $f(R,T)$ gravity

In the present work, we have searched the existence of anisotropic and non-singular compact star in the $f(R,T)$ gravity by taking into account the non-exotic equation of state (EoS). In order to obtain the solutions of the matter content of compact object, we assume the well known barotropic form of EoS that yields the linear relation between pressures and energy density. We propose the existence of non-exotic compact star which shows the validation of energy conditions and stability with in the $f(R,T)$ extended theory of gravity perspective. The linear material correction in the extended theory the matter content of compact star remarkably able to satisfies energy condition. We discuss various physical features of compact star and show that proposed model of stellar object satisfies all regularity conditions and is stable as well as singularity-free.

gr-qc↗

arXiv2020

Study of gravastars under $f(\mathbb{T})$ gravity

In the present paper we propose a stellar model under the $f(\mathbb{T})$ gravity following the conjecture of Mazur-Mottola~[Report number: LA-UR-01-5067 (2001); Proc. Natl. Acad. Sci. USA 101 (2004) 9545] known in literature as {\it gravastar}, a viable alternative to the black hole. This gravastar has three different regions, viz., (A) Interior core region, (B) Intermediate thin shell, and (C) Exterior spherical region. It is assumed that in the interior region the fluid pressure is equal to a negative matter-energy density providing a constant repulsive force over the spherical thin shell. This shell at the intermediate region is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zeldovich's conjecture of stiff fluid~[Zeldovich, Mon. Not. R. Astron. Soc. 160 (1972) 1], does nullify the repulsive force exerted by the interior core region for a stable configuration. On the other hand, the exterior spherical region can be described by the exterior Schwarzschild-de Sitter solution. With all these specifications we have found out a set of exact and singularity-free solutions of the gravastar which presents several physically interesting as well as valid features within the framework of alternative gravity.

gr-qc↗

arXiv2020

Conformally symmetric traversable wormholes in modified teleparallel gravity

In this paper, we consider wormhole geometries in the context of teleparallel equivalent of general relativity (TEGR) as well as $f(T)$ gravity. The TEGR is an alternative geometrical formulation of Einstein's general relativity, where modified teleparallel gravity or $f(T)$ gravity has been invoked as an alternative approach for explaining an accelerated expansion of the universe. We present the analytical solutions under the assumption of spherical symmetry and the existence of a conformal Killing vectors to proceed a more systematic approach in searching for exact wormhole solutions. More preciously, the existence of a conformal symmetry places restrictions on the model. Considering the field equations with a diagonal tetrad and anisotropic distribution of the fluid, we study the properties of traversable wormholes in TEGR that violates the weak and the null energy conditions at the throat and its vicinity. In the second part, wormhole solutions are constructed in the framework of $f(T)$ gravity, where $T$ represents torsion scalar. As a consistency check, we also discuss the behavior of energy conditions with a viable power-law $f(T)$ model and the corresponding shape functions. In addition, a wide variety of solutions are deduced by considering a linear equation of state relating the density and pressure, for the isotropic and anisotropic pressure, independently of the shape functions, and various phantom wormhole geometries are explored.

gr-qc↗

arXiv2020

Exploring physical properties of compact stars in $f(R,T)-$gravity: An embedding approach

Solving field equations exactly in $f(R,T)$ gravity is one of the difficult task. To do so, many authors have adopted different methods such as assuming both the metric functions, an equation of state (EoS) and a metric function etc. However, such methods may not always lead to well-behaved solutions and thereby rejection of the solutions may happen after complete calculations. Indeed, very recent works on embedding class one methods suggested that the chances of arriving at the well behaved-solution is very high thereby inspired us to used it. In class one approach, we have to ansatz one of the metric potentials and the other can be obtain from the Karmarkar condition. In this paper, we are proposing new class one solution which is well-behaved in all physical points of view. We have analyzed the nature of the solution by tuning the $f(R,T)-$coupling parameter $χ$ and found that the solution results into stiffer EoS for $χ=-1$ than $χ=1$. This is because for lesser values of $χ$, velocity of sound is more, higher $M_{max}$ in $M-R$ curve and the EoS parameter $ω$ is larger. The solution satisfy the causality condition, energy conditions, stable and static under radial perturbations (static stability criterion) and in equilibrium (modified TOV-equation). The resulting $M-R$ diagram from this solution is well fitted with observed values of few compact stars such as PSR J1614-2230, Vela X-1, Cen X-3 and SAX J1808.4-3658. Therefore, for different values of $χ$, we have predicted the corresponding radii and their respective moment of inertia from the $M-I$ curve.

gr-qc↗

arXiv2020

Subatomic particle as the quantum universe

Wheeler-Dewitt equation for the wave function of the universe appeared long ago in an approach to quantization of gravity. Presently, the universe considered as the microuniverse, very tiny universe compared to the outer universe to which it belongs. This tiny universe is, thus, supposed to be the subatomic particle (elementary particle) in the universe we live in. It is possible here to convert the wave function of this microuniverse satisfying Wheeler-Dewitt equation into the wave function of the quantum (subatomic) particle, which is shown to satisfy Schrödinger equation. The inverse of the length scale indicating smallness of the particle appears in the Schrödinger equation being the mass of the particle. Thus, the subatomic particles are shown here to be the quantum universes.

physics.gen-ph↗

arXiv2019

The Finslerian quantum cosmology

We present a Friedmann-Robertson-Walker (FRW) quantum cosmological model within the framework of Finslerian geometry. In this work, we consider a specific fluid. We obtain the corresponding Wheeler-DeWitt equation as the usual constraint equation as well as Schrödinger equation following Dirac, although the approaches yields the same equation of time independent equation for the wave function of the universe. We provide exact classical and quantum mechanical solutions. We use the eigenfunctions to study the time evolution of the expectation value of the scale factor. Finally we discuss the physical meaning of the results.

physics.gen-ph↗

arXiv2019

Neutron star under homotopy perturbation method

We obtain a mass function solving the Tolman-Oppenheimer-Volkoff (TOV) equation for isotropic and spherically symmetric system via homotopy perturbation method (HPM). Using the mass function we construct a stellar model which can be determined from the equation of state (EOS) parameter ($ω$) and a model parameter ($n$). With the help of Einstein field equations we develop three solutions which can describe different properties and the core-crust structure of neutron star (NS). Solution I is valid for NS having the inner and outer radius near the surface of the star. The star is physical up to the inner radius whereas negative density occurs and the energy conditions are violated in the upper region from the inner to outer radius. Solution II represents NS with high gravitational redshift as well as compactification factor. All the features of NS can be given by solution III which involves only the EOS parameter. Our model predicts maximum mass for a NS with the central density $5.5\times10^{15}~g/cm^{3}$ and surface redshift 0.69 is to be $2.01~M_\odot$ for the EOS parameter $ω=0.73$. The predicted range for the surface redshift is $0.57<Z_s<1.95$ for the allowed ranges $8.4<n<10.9$ and $1/3<ω<1$ in the presented NS model.

gr-qc↗

arXiv2019

Einstein's cluster mimicking compact star in the teleparallel equivalent of general relativity

We present a physically plausible solution representing Einstein's cluster mimicking the behaviors of compact star in the context of teleparallel equivalent of general relativity. The Teleparallel gravity (TEGR) is an alternative formulation of gravity which uses tetrads as the dynamical variables. We focus on two particularly interesting scenarios. First, we develop the Einstein clusters in TEGR field equations using effective energy-momentum tensor for diagonal as well as off-diagonal tetrad. We then study the clusters in modified $f(T)-$gravity for anisotropic fluid distribution. Based on these two theories, we further study the solution without net electric charge and then for charged solution. For charge parameter $k \rightarrow 0$, the charged solution reduces to neutral one. Our calculations show that when charge increases, the stiffness of the EoS also increases. This is due to increase in adiabatic index and sound speed approaching speed of light. When the charge increase beyond a certain limit ($0\le k \le 1.3 \times 10^{-5}$ and $0\le k \le 1 \times 10^{-6}$), the compactness parameter crosses the Buchdahl limit i.e. $2M/R>8/9$ and the solution start violating the causality condition. We test the Tolman-Oppenheimer-Volkoff (TOV) limit for such compact objects. We analyze the static stability criterion of the Einstein clusters for both charged and uncharged case, and the stability of such compact objects is enhanced by the presence some net electric charge. Finally, we compare our solution for pure general relativity. As a result, we concluded that the Einstein cluster solution do exist in pure GR, however, physically unfit to mimic compact stars. We have also extend our findings by assuming the diagonal or off-diagonal tetrad and specific case of $f(T)$. In such models, Einstein's cluster solutions do exist however can't mimic the properties of a compact star.

gr-qc↗

arXiv2019

Noncommutative black hole in the Finslerian spacetime

We study the behavior of the noncommutative radiating Schwarzschild black hole in the Finslerian spacetime. The investigation shows that black hole possesses either (i) two horizons, or (ii) a single horizon, or (iii) no horizon corresponding to a minimal mass. We obtain that the minimal mass significantly changes with the Finslerian parameter, keeping minimal horizon remain unchanged. It turns out that under Finslerian spacetime, the maximum temperature before cooling down to absolute zero varies with Finslerian parameter. We then study the stability of the black hole by analyzing the specific heat and free energy. The energy conditions, their violation limit also scrutinized. Our findings suggest a stable black hole remnant, whose mass and size are uniquely determined in terms of the Finslerian parameter $\overline{Ric}$ and noncommutative parameter $θ$. The physical relevance of these results are discussed in a brief.

physics.gen-ph↗

arXiv2019

Constraining values of bag constant for strange star candidates

We provide a strange star model under the framework of general relativity by using a general linear equation of state (EOS). The solution set thus obtained is employed on altogether 20 compact star candidates to constraint values of MIT bag model. No specific value of the bag constant ($B$) a-priori is assumed rather possible range of values for bag constant is determined from observational data of the said set of compact stars. To do so the Tolman-Oppenheimer-Volkoff (TOV) equation is solved by homotopy perturbation method (HPM) and hence we get a mass function for the stellar system. The solution to the Einstein field equations represents a non-singular, causal and stable stellar structure which can be related to strange stars. Eventually we get an interesting result on the range of the bag constant as 41.58~MeV~fm$^{-3}< B <$319.31~MeV~fm$^{-3}$. We have found the maximum surface redshift $Z^{max}_{s}=0.63$ and shown that the central redshift ($Z_c$) can not have value larger than $2k$, where $k=2.010789 \pm 0.073203$. Also we provide a possible value of bag constant for neutron star (NS) with quark core using hadronic as well as quark EOS.

gr-qc↗

arXiv2019

Possible formation of wormholes from dark matter in an isothermal galactic halo and void

It is well known that traversable wormholes are valid solutions of the Einstein field equations, but these structures can only be maintained by violating the null energy condition. In this paper, we have obtained such wormhole solutions in an isothermal galactic halo, as well as in a void. We have shown that the null energy condition is violated, with the help of a suitable redshift function obtained from flat galactic rotation curves.

physics.gen-ph↗

arXiv2019

A generalized Finch-Skea class one static solution

In the present article, we discuss relativistic anisotropic solutions of the Einstein field equation for the spherically symmetric line element under the class I condition. To do so we apply the embedding class one technique using Eisland condition. Within this approach, one arrives at a particular differential equation that links the two metric components $e^ν$ and $e^λ$. In order to obtain the full space-time description inside the stellar configuration we ansatz the generalized form of metric component $g_{rr}$ corresponding to the Finch-Skea solution. Once the space-time geometry is specified we obtain the complete thermodynamic description i.e. the matter density $ρ$, the radial, and tangential pressures $p_r$ and $p_t$, respectively. Graphical analysis shows that the obtained model respects the physical and mathematical requirements that all ultra-high dense collapsed structures must obey. The $M-R$ diagram suggests that the solution yields stiffer EoS as parameter $n$ increases. The $M-I$ graph is in agreement with the concepts of Bejgar et al. \cite{bej} that the mass at $I_{max}$ is lesser by few percent (for this solution $\sim 3\%$) from $M_{max}$. This suggests that the EoSs is without any strong high-density softening due to hyperonization or phase transition to an exotic state.

physics.gen-ph↗